np-complete


Knapsack for each weight having multiple values - Is it possible to solve?


I have a 0/1 minimization Knapsack problem with a sum equality constraint. However, more interestingly, my weights can take values between 0:15. My question is, can I really solve this problem in polynomial time and, if yes, how?
By the way, I have n=100 items, all of whose weights (w_i) can be between 0 and 15. In addition, my values (v_i) change for each item when the weight changes in the given range. Also my equality value is 212.

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